{"paper":{"title":"Asymptotic properties of zeros of Riemann zeta function","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Juan Arias de Reyna, Yves Meyer","submitted_at":"2025-07-09T19:54:26Z","abstract_excerpt":"We try to define the sequence of zeros of the Riemann zeta function by an intrinsic property. Let $(z_k)_{k\\in \\mathbb{N}}$ be the sequence of nontrivial zeros of $\\zeta(s)$ with positive imaginary part. We write $z_k= 1/2+i\\tau_k$ (RH says that these $\\tau_k$ are all real). Then the sequence $(\\tau_k)_{k\\in \\mathbb{N}},$ satisfies the following asymptotic relation \\[\\sum_{k\\in\\mathbb{N}}\\frac{2x}{x^2+\\tau_k^2}\\simeq \\frac12\\log\\frac{x}{2\\pi}+\\sum_{n=1}^\\infty \\frac{a_n}{x^n},\\,\\,x\\to +\\infty\\] where $a_{2n+1}=2^{-2n-2}(8-E_{2n})$, $a_{2n}=(1-2^{-2n+1})B_{2n}/(4n).$ Are there other sequences $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07253","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07253/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}